Amazon is No. 1. Who’s next in cloud computing?

Amazon Web Services is, by all accounts, the largest cloud service provider by far, although good luck finding third-party numbers to verify that. Amazon, like most of the big cloud providers, doesn’t disclose much about current or planned data centers.

So, stipulating AWS as No. 1, here are seven cloud rivals that could give it a run for its money over the next few years.

1: Rackspace: While Rackspace encompasses managed services and pure hosting businesses, it’s also a major cloud provider with actual, paying customers. Measuring by revenue and VMs, Rackspace currently has a lock on the No. 2 slot by a wide margin, said Gartner analyst Lydia Leong. As one data point, Rackspace public cloud revenue rose to $189 million in fiscal year 2011, up from $100M the previous year. Going forward, that business should only grow as Rackspace brings more OpenStack implementations online.

2: Google: If you’re talking number of physical servers, Google could already be the biggest cloud player. As for paying customers? That’s harder to discern. Google is one of the few companies that can (and does) invest in the pure computing firepower to contend with AWS. If you count all that Google Apps and Gmail storage, then Google’s obviously a huge player. The Google App Engine platform-as-a-service is still around but isn’t a factor for business developers.

3: Microsoft: Two-year-old Windows Azure has big capacity, but actual traction is unclear — but it is clear Microsoft is going for the gusto. Microsoft just launched an Azure-focused startup accelerator in Israel to help boost demand. Next week, it is expected to announce timing for the first of its ERP products — actually the first of any of its major products — to run on Azure. And, going forward, Microsoft Azure’s embrace of Hadoop could attract more of the next-generation big-data workloads that the cloud vendors compete for.

4: IBM: IBM SmartCloud is coming up fast on AWS and Rackspace even now, according to one cloud storage expert. That news surprised me but probably shouldn’t have, given IBM’s size and resources. And face it: IBM knows data centers. Like Microsoft, it is bringing Hadoop into its cloud with its InfoSphere BigInsights service.

5: Hewlett-Packard: HP’s been all over the map on cloud plans, promising an Azure-based implementation a few years ago that has gone nowhere and more recently standing up an OpenStack-based public cloud. Zorawar “Biri” Singh, SVP for HP cloud services, told the New York Times last week that HP’s cloud will add features and capabilities beyond what AWS provides. HP has also said it wants to challenge AWS for the hearts and minds of cloud developers. HP has had its share of woes lately, but it’s still a tech power, and provided the cloud is a priority with new management, it would be hard to rule out.

6: VMware: VMware’s vCloud already runs a ton of clouds for third-party providers, and the company’s Cloud Foundry platform-as-a-service is gaining traction. All of that plus the Mozy cloud storage service, which VMware manages for parent EMC, means that the company — which dominates server virtualization inside the firewall — is gaining a pretty impressive toehold in the cloud beyond as well.

7: Facebook: Don’t laugh. It’s a wildcard, but Facebook is putting serious sweat into data centers. And it’s applying lessons learned to the Open Compute Project, which aims to apply open source development to hardware design. With more than 800 million users, Facebook knows a thing or two about cloud infrastructure. True, Facebook doesn’t offer cloud services now, but then again, Amazon used to just sell books. Facebook could evolve into many things. GigaOM’s Derrick Harris has already suggested that Facebook could be your next software vendor.

Scrappy competitors could make a play, but…

“To compete with AWS you would need three things: Billions to invest, the wherewithal to manage technology on a massive scale and freedom from legacy constraints. Google and Microsoft surely have the money as well as the technology chops, but both are constrained by commitments to their valuable core businesses. Who might come in to compete out of the blue? Maybe Facebook, if they were looking for another line of business,” said Robert Shear, president of Greystone Solutions, a Boston consultancy that uses AWS for most of its development and deployment work. “My guess is that AWS will keep on growing until they bump up against anti-trust limitations in the US and the EU.”

So there you have it: seven contenders who could duke it out for the No. 2 spot in cloud services over time — and maybe even battle AWS for the top spot. Who am I missing here?